How do you use $csctheta=4$ to find $tantheta$ ?

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How do you use $csctheta=4$ to find $tantheta$ ?

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Answer 1 · 2018-06-03T21:41:16

$tan t = +- sqrt17/4$

Explanation:

$csc t = 1/sin t = 4$
$sin t = 1/4$
t could be either in Quadrant 1 or Quadrant 2.
$cot^2 t = 1/(1 + sin^2 t) = 1/(1 + 1/16) = 16/17$
$cot t = +- 4/sqrt17$ .
$tan t = 1/(cot t) = +- sqrt17/4$
If t lies in Quadrant 1 --> tan t is positive
If t lies in Quadrant 2 --> tan t is negative.

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How do you use $csctheta=4$ to find $tantheta$ ?

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